The grades on a history midterm at Santa Rita are normally distributed with $\mu = 76$ and $\sigma = 3.0$. Ben earned a $71$ on the exam. Find the z-score for Ben's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Ben's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{71 - {76}}{{3.0}}} $ ${ z \approx -1.67}$ The z-score is $-1.67$. In other words, Ben's score was $1.67$ standard deviations below the mean.